Dear NA friends,

I don’t normally sink so low as to send you an image from a movie, but this is irresistible. Kate and I just saw The Martian, in which Matt Damon is stuck on Mars and likely to die. But then the very cool young JPL astrophysicist genius Rich Purnell has the idea of slingshotting a spacecraft around Earth and back to Mars at great speed. Will it work? Cool young Purnell goes to the computer to run the math. He presses Enter, waits a tense moment, and then in one of the film’s big dramatic moments, gets this response on the screen,

==================
| CALCULATIONS CORRECT |
==================

Isn’t this delicious? It’s not every day that Hollywood shows the world the excitement of numerical computation.

[16 May 2016]

In this awful Trump election year, Republicans are announcing that they won’t vote for him; and of course, most of them add, they couldn’t possibly vote for Hillary either. The latest is Miami mayor Tomás Regalado. Today the New York Times reports that Regalado says he’s going to sit this one out.

The idea of sitting out an election gives another illustration of the strange disconnect between the mathematics and the psychology of voting. Mathematically, for a Republican to not vote for anybody has exactly the same effect as voting for Hillary, except with half the magnitude. Who would want their vote to be cut in half? But the human truth of voting has little to do with the mathematics. We all construct personal narratives of how we will or won’t vote, and out of millions of narratives, somehow or other, a president is elected.

[31 May 2016]

Women’s brains are 10% smaller than men’s, yet the sexes are equally intelligent. It might not have turned out like this.  It’s easy to imagine a world in which natural selection had made men brighter than women. The image is an awful one, a dystopia in which the relationship between the sexes would surely have been that of master and slave.  Thank goodness it didn’t turn out like that.

But actually, it did turn out like that: not with brains, but with brawn. We’re so used to men being bigger and stronger that we don’t regard this disparity with horror. Yet most men can dominate most women physically, and I believe this is the main reason why in most societies throughout history, the men have been in control. Why do men dominate women? Because they can.

In recent generations, thanks to the cognitive demands of advancing civilization, we are beginning to rise above the physical differences and approach equality. It might not have turned out like this. If the dimorphism had been in brains rather than brawn, the advance of civilization might have increased the inequality between the sexes rather than diminishing it.

[22 April 2011]

In Madrid this week, I spent a lot of time looking at Las Meninas.  What a friend it became!

A salient feature of art and literature, and a recurring theme in these notes, is the power of ambiguity.  The experience of a great work may be due half to the artist, who brings so much to the canvas, and half to the viewer, in whose eye and mind the image resonates.  Las Meninas has become my archetypical example of this synergy.  Standing in front of it in that great hall of the Prado, I felt that Velazquez and I were working together to create this viewing experience.

It is key that he is looking at us. He’s daring us with the question, what do you think of this?  What do you make of the dog, and the dwarf, and the cavernous dark upper half of my painting?  Can you imagine the secrets I know of this crazy decadent court of Philip IV?

Yet there is so much Velazquez did not know!  He did not know that Britain and its colonies in America would build a new world as Spain declined ever further. He did not know that the infanta Margarita would die at age 21.  It may be just my fancy, but I like to think that Velazquez had a sense of the uncertainty of the future and the genius to craft a work that would take strength from that uncertainty.

[3 April 2016]

What’s the smallest nonprime that is not obviously nonprime? For Ramanujan the answer would have been in the thousands, but for the rest of us, I think it’s 91. The sequence of nonobvious nonprimes runs 91, 119, 133, 143, 161, 187,….

Here’s my reasoning. If a number is divisible by 2, 3, or 5, that’s obvious, and if it is 11 times a single digit, that’s obvious too. Also, perfect squares are pretty familiar. This leaves us with 7•13, 7•17, 7•19, 11•13, 7•23, 11•17,….

[14 May 2016]

Oxford dons are expected to have glittering conversations at high table, and we had a good one today.

One of the fellows mentioned a psychologists’ theory that an infant first understands the number 2, then later the number 3, then later the number 4, before finally figuring out the general notion of number.  However, she said, she and her husband hadn’t been able to detect stages 3 or 4 in their own little boy.

I mentioned the physicists’ theory of the period-doubling transition to chaos.  This involves an infinite succession of orbits, each one 4.669… times shorter than the last (Feigenbaum’s constant).  Maybe the little one went through all the number stages, but too fast to observe?

It was David Wallace who wrapped up the interchange with a philosophers’ twist.  If an infant masters the number 2 in one week, the number 3 in the next half-week, the number 4 in the next quarter-week, and so on, why then, in a fortnight he’ll have mastered all the numbers, an infinite collection of specific notions in finite time!  Who needs the general concept?

[14 April 2016]

I got my first pair of varifocals a few months ago. When I put them on I felt I was swimming in a sea of blur and I was tempted to abandon the experiment.  Nathaniel said, don’t worry, in a few days you’ll be used to them and the world will look good again.

He was right.  My brain adjusted comprehensively and my new eyesight quickly became the new normal.  On a glorious walk along the South Downs Way yesterday, for example, I almost never noticed that the focussed fraction of my field of vision is half what it was a year ago.

Your first thought may be pleasure at how easily our brains adjust, but your second should be one of horror.  How diabolically our brains disguise our declining powers!  My visual input is half what it was a year ago, and I don’t notice.  It’s probably a tenth what it was when I as a teenager, and I don’t notice that either.  It’s a safe bet the power of my thought has diminished too.  As the engine slows down, occasionally there are puzzling artifacts out there in the periphery, but for the most part, we don’t notice.

[11 April 2016]

Every adult knows that the matter of God is a serious one, quite unrelated to the case of Santa Claus, who is a harmless invention for children.

Kate and I saw a millennium-scale version of this disparity on display this week in hall after hall of the Prado.  Half the paintings of the Renaissance seem to depict stories of the Christian holy family and the saints, and the other half, stories of Greek and Roman gods and mortals.  In the first category, we have for example Fra Angelico’s beautiful “Annunciation”, which shows Mary being dazzled by a sunbeam of gold, symbolic of God impregnating her.  This led to the birth of Jesus, who was both god and man.  In the second category, we have Titian’s beautiful “Danaë and the shower of gold”, which shows Danaë being dazzled by a cascade of gold coins, symbolic of Zeus impregnating her.  This led to the birth of Perseus, who was half god and half man.

I doubt one Prado visitor in a hundred notices how indistinguishable the Christian and Greek/Roman stories would be to the proverbial Martian.  Even then, to make the parallel feels boorish and simplistic. One is tempted to think, well, that’s very clever, but of course, the two cases are completely different.  Everyone knows those Greek and Roman stories are just stories!  When in doubt of your doubt: remember Fra Angelico’s Mary and Titian’s Danaë.

[3 April 2016]

We are machines, of course, but with the curious feature that we can see ourselves from the inside.

It was strange to see myself from the inside just now here in the guest rooms of St. John’s College, above the candy shop.  There are two toilets, side by side, interchangeable. Yesterday evening I needed the toilet and arbitrarily chose the one on the right. Today I needed the toilet again and realized there was no choice in the matter at all — my steps were quite autonomically taking me back to the same one I had used yesterday.

Why?  Why in the world must I use the same toilet on day 2 as on day 1? Presumably because, for some excellent reason of natural selection, we are built like this.

As a matter of principle, just to show I could, I overrode the machine and used the one on the left.

[7 January 2016]

The sun is 100,000,000 miles away, 1,000,000 miles across, whereas the moon is 100,000 miles away, 1000 miles across.  (All numbers are rounded to the nearest power of 10.) Our eyes miss these vast scales entirely and see both objects as of comparable size and distance, much closer than they really are. They seem, what, maybe 10 miles away and 1/10 mile across?

I’ve long been interested in what I call “the other moon illusion”: if you consider the sun and moon together in the sky, you will judge, the moon should look fuller!  This illusion results from failure to perceive that the sun is further away than the moon.  It amuses me to note that to eliminate it, we wouldn’t have to perceive the truth, that the sun is a thousand times further than the moon, let alone that it is ten million times further than it looks.  If we could only perceive it as 20 miles away instead of 10, that would be enough.

[7 January 2016]